Two British nationals were among more than 30 people killed by a suicide bomber at Moscow's busiest airport, according to Russian investigators.

A Foreign Office spokesman said he was aware of the reports but could not confirm the deaths.

He said: "We have a consular team on the ground and we are urgently investigating."

Russian investigative committee spokesman Vladimir Markin has not identified the British victims who died in the explosion at Domodedovo airport.

The blast saw more than 30 people killed and almost 170 injured.

David Cameron offered Britain's "complete support" in dealing with the terror attack in a telephone call with Mr Medvedev, Downing Street said.

"The Prime Minister utterly condemned today's explosion at Domodedovo airport. He offered his condolences and sympathies to all those who had been affected by what he described as an appalling attack," a Number 10 spokeswoman said.

"The Prime Minister assured President Medvedev of his complete support and said that the Russian authorities could count on Britain for any assistance they needed.

"The Prime Minister made clear that the people of Britain stood with the people of Russia in the face of these events and said that 'we should never allow the terrorists to win'."

Two flights from London Heathrow had arrived at Domodedovo airport shortly before the explosion in the international arrivals hall.

The Foreign Office said consular staff, including the consul general, were at the airport.

Reports on Russian television suggested the bomber shouted "I'll kill you all!" before detonating the device.

Witnesses said he walked into the airport carrying a suitcase and the blast sprayed shrapnel, screws and ball bearings across the terminal.

The Interfax news agency cited law enforcement sources saying the head of the suspected bomber had been found.

No one immediately claimed responsibility.

Airport spokeswoman Yelena Galanova said 35 people were killed but the Emergencies Ministry said there were 31 fatalities with 74 people hospitalised and 94 given medical treatment.

Domodedovo was briefly closed to air traffic immediately after the blast but soon reopened.

Artyom Zhilenkov, a 35-year-old driver, said: "I saw the suitcase, the suitcase was on fire.

"So, either the man blew up something, or something went off on the man's body, or the suitcase went off.

"The guy standing next to me was torn to pieces."

British witness Mark Green told BBC News: "As we were picking up the bags to put them into the back of the car, there was an almighty explosion. It reverberated through our bodies."

Footage posted on YouTube showed the aftermath of the incident, with a mass of bodies and luggage strewn on the floor of the smoke-filled terminal.

One shell-shocked man can be seen briefly, standing behind his luggage trolley among the carnage, looking from side to side.

Foreign Secretary William Hague said: "On behalf of the UK, I send condolences to all those who have lost relatives or been injured.

"British officials are in urgent contact with the Russian authorities to establish the facts and to provide consular support to any British nationals who may have been affected."

British Airways operates three flights daily from the airport while BMI operates two flights.

A BA spokeswoman said flight BA872 landed at 3.46pm local time with 165 passengers on board, adding: "We are aware of the incident at Moscow's Domodedovo airport and are speaking to our teams at the airport to establish further information."

BA confirmed that BA874, which left London en route to Moscow at 12.30pm, had turned back towards the UK.

A BMI spokeswoman said flight BD891 landed at 4.33pm local time with 97 passengers on board. The blast went off shortly afterwards.

The spokeswoman said all the passengers had disembarked before the incident, adding: "All the BMI crew are accounted for. We are waiting for information about whether the passengers were caught up in the incident from the authorities in Moscow."

She continued: "BMI has taken the decision to cancel flight BD895 due to depart this evening and the return flight BD896 departing Moscow at 6.30am tomorrow."

Domodedovo is 26 miles south east of the centre of Moscow and is the largest of the capital's three major airports, serving more than 22 million people last year.

Following the incident, the Foreign Office updated its travel advice, to say the airport was closed and passengers should not travel there.